Bipartisan senators near a limited immigration deal

Washington (CNN)After two days of procedural fits and starts, the Senate finally moved Wednesday to begin debate on immigration reforms aimed at resolving what to do with undocumented immigrants who came to the US as children whose legal status in the country may soon expire.

The Senate approved a motion by voice vote to begin debate, and as they were doing so, a group of Republican senators said there was a possible deal in sight.

Immigration state of play: 48 hours of Senate debate to go

Democrats demanded the debate on immigration — and even briefly shut down the government to try to force it — but have yet to agree to a compromise bill with a group of Republicans that could get 60 to pass the chamber.

Those talks were still underway in the office of Sen. Susan Collins, R-Maine, when the floor debate formally opened. Members emerged from Collins’ office and said they had the contours of an agreement that would be “two pillars.” It would protect DACA recipients in exchange for a major boost in border security.

Sen. Jeff Flake, R-Arizona, told reporters that he expects the bipartisan coalition would have a finished proposal to announce Wednesday, a major breakthrough after weeks of negotiations.

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“Seems to me the consensus is to have big border security and big DACA,” said Sen. Lindsey Graham, R-South Carolina.

But Graham told reporters that any deal would not include a pathway for the parents of DACA recipients.

“If you deal with the parents now you lose a lot of Republicans. If you try to do the breaking chain migration now you lose a lot of Democrats,” said Graham.

“It would be a two-pillar bill,” he added.

Bill from Colorado senators

Also Wednesday, a new effort emerged from the bipartisan Senate delegation from Colorado — Sens. Cory Gardner and Michael Bennet.

The amendment was offered Wednesday and represented a narrow approach to a deal — a pathway to citizenship for young undocumented immigrants similar to other proposals and the creation of a $25 billion trust for border security. The bill would also restrict that money to only its designated purpose and require annual reporting from the government on the border.

The bill also included a couple of small pieces to gain additional support.

It would boost the number of immigration judges and attorneys to try to work down the immigration court backlog, which contributes to undocumented immigrants being left in the US for years as they await hearings, and it would also make voluntary worker verification systems permanent — a concession to Republicans but far short of the mandatory use of the e-verify system for every employer that hardline conservatives have long demanded.

Trump reinforces stance

It’s still unclear if the bipartisan approach would be able to garner the needed 60 votes to pass, however.

And President Donald Trump has been clear that he doesn’t want anything short of a four-pillar solution– one that includes border security, protections for DACA recipients, an end to the diversity lottery and a massive overhaul of the country’s legal immigration system.

RELATED: Trump issues fresh opposition to short-term DACA bill

The inability of the bipartisan group to put a bill on the floor for a vote has frustrated Republicans who said they were stunned that after months of negotiations, the group wasn’t ready. Many Republicans back a bill from Sen. Chuck Grassley, R-Iowa, that is supported by Trump, which would lead to a pathway for citizenship for 1.8 million people in return for $25 billion for border protection and significant changes to “chain” migration and the diversity visa lottery. That measure is also unlikely to get 60 votes.

But on a call with reporters Wednesday, White House officials declined to explicitly answer a question about whether Trump would veto a proposal that doesn’t match what the administration has demanded, but it’s unlikely a bill the President opposes would pass both houses of Congress.